Sophisticated seismic migration programs require velocity models in terms of instantaneous velocity (the velocity of seismic waves at a particular location in the earth). Unfortunately, no means exist for directly measuring this instantaneous velocity in the frequency band of seismic data. Instead one gathers data, which are indirectly sensitive to instantaneous velocity, and then inverts these data to determine the migration velocity model. Table 1 lists the types of data that are conventionally gathered and their relationship to the instantaneous velocity (v.sub.inst).
TABLE 1 Types of data gathered for estimating instantaneous velocity and their relationships to instantaneous velocity. Data Gathered Approximate Relation to Instantaneous Velocity Surface Seismic Root-Mean-Square average of v.sub.inst from surface Vertical Checkshot Average of (1/v.sub.inst) from surface Sonic Log v.sub.inst but far outside the seismic frequency band Offset Checkshot Average of 1/v.sub.inst along migration ray paths
Excepting sonic logs, the sources of velocity information depend on some running average of the instantaneous velocity. Thus, these measurements are heavily filtered versions of the needed information and converting these measurements to instantaneous velocity is an unstable process. Small errors in the measurements produce large errors in instantaneous velocity.
[Note--where checkshots are the source of the measured "velocity" data or information, such data or information will actually be traveltimes, not velocities; however, for purposes of this patent application, the term "measured velocity data" and equivalent or similar terms will be understood to include or mean traveltime data in the case of checkshots, and conversely terms such as "model-predicted velocity data" will be understood to include or mean traveltimes calculated from the velocity model where the context requires. Such traveltimes are determined by tracing ray paths in the velocity model, starting at the checkshot source and proceeding to the checkshot receiver. Similarly other types of available data may be used to constrain velocity models, e.g. well tops data, which are distances from the surface to various rock layers, as measured in a well bore. All such approaches are intended to be within the scope of the present invention.]
It would be desirable to incorporate all of these sources of velocity information when developing migration velocity models, because the strengths of one source often offset the weaknesses of another. Unfortunately, the different sources of velocity information usually give inconsistent estimates of the instantaneous velocity. This inconsistency may be due to some physical principle that is being ignored (e.g., anisotropy), or it may be simply due to the instability encountered when converting from the measured velocity information to instantaneous velocity. The latter situation requires velocity estimation methods that are robust with respect to these instabilities.
The conventional method for converting from the velocity one can measure to instantaneous velocity begins by picking the velocity information as a function of depth. This is a process first of interpretation, primarily distinguishing signal from noise, and then digitizing the data. In the case of surface seismic data, the velocity information will be RMS velocity, and for vertical checkshot data, it will be vertical traveltime. These measurements are then converted to instantaneous velocity by using an analytic formula. For surface seismic velocities, the formula is the Dix equation. This process tends to be unstable, such that small errors in the measured velocity data can generate relatively large errors in the calculated instantaneous velocity. For vertical checkshot measurements, the instantaneous velocity is simply the depth derivative of the measurements. As with the Dix equation, applying a derivative to the measured data is an unstable process. Moreover, it is typical to find that the different sources of velocity information yield different values for the instantaneous velocity. To overcome this problem, one of the information sources is usually picked and the others discarded, or an ad hoc calibration adjustment may be developed to make the sources agree. The resulting velocity model usually has unreasonably large vertical and lateral variability, so it is necessary to smooth the model.
There are three problems with this conventional velocity model building method:
1. The ad hoc calibration may be simply correcting for the fact that the conversion to instantaneous velocity is unstable. If that is the case, the calibration is unlikely to be accurate.
2. After smoothing, the model may no longer be consistent with the measured velocity information. Even worse, it is difficult to control the smoothing in a geologically reasonable manner. Typically, only the lengths of the smoothing operators can be controlled. This method gives no direct control over the migration velocity model.
3. This method requires picking velocities at a large number of locations so that the smoothing process is statistically reasonable. This picking is a very time consuming process.
Another popular method of converting measured velocity information to migration velocity models is tomography. This method uses an automated minimization approach to find a model that is consistent with all the velocity data. Constraints can be included that force the model to be smooth, usually at little cost to the data fit. This method should avoid the first two pitfalls of the conventional method discussed above. Tomography should be able to find a smooth model that still is consistent with the measured data. Also, incorporating different sources of velocity information into tomography should enhance the resulting model, unless the model does not account for physical causes which make the sources of velocity information inconsistent (e.g., anisotropy). Inconsistency of information, due simply to the instability of the inversion, should not be a problem for tomography.
However, being an automated method, tomography does not give the user direct control over the migration velocity. In particular, this technique may have difficulties in regions of poor seismic data quality. Furthermore, tomographic procedures may be too expensive to apply to three-dimensional (3-D) seismic data. (3-D tomographic inversion methods are not often applied in production processing and are still the subject of a considerable amount of research.) Thus, when it becomes widely available, tomography may be the method of choice in areas having good data quality. In the meantime less expensive methods, based on manual updating of velocity models, are required.
From the foregoing, it can be seen that an improved method for constructing instantaneous velocity models is needed. Such a method should provide for comparison of model velocities to available velocity data in the latter's domain to avoid inherent instabilities in converting measured data to instantaneous velocity. Such a method should generate a smoothly varying velocity model, thereby eliminating the need to apply artificial smoothing operators, which smooth the model in a geologically unreasonable manner and disrupt consistency with the measured data. Such a method should be manual as opposed to automated, thereby enabling the operator to make decisions such as how to treat regions of poor data quality or how to make simplifying assumptions with minimal loss of accuracy, judgments that are too difficult presently to program into automated methods in a satisfactory way. Because the desired improved method needs to be a manual method, such a method must be fast and efficient, which means that it must involve adjusting velocities at relatively few locations, and which also means that there must be a quick visual and comprehensive method of adjusting the model and comparing it to actual data in order to perfect the model and ensure its conformity to measured data. Moreover, such an improved method must be fast enough to handle large 3-D data sets without the extreme time and expense of present automated methods. The present invention satisfies these needs.